A. Place the Subtrahend under the Minuend, units under units, tens under tens, and so on.

5. Q. What is the next step

A. Draw a line below; then begin at the right hand, and subtract each figure of the less number from the figure above it, and place the remainder directly below.

6. Q. When the figure in the lower number is greater than that of the upper number from which it is to be taken, what is to be done?

A. Borrow one from the next superior colemn, which is equal to ten of the inferior; suppose this 10 to be added to the upper figure; and from the number so increased take the lower; set down the remainder and carry one to the next lower figure, to pay for that which you borrowed, and subtract as before, and so on through the whole.

7. Q. How is Subtraction proved?

A. Add the Remainder and Subtrahend together, and if the sum of them correspond with the Minuend, the work is supposed to be right.

2d. The American Independence was declared July 1775. How many Years since? July 1824. Ans. 49. 3d. A owes 375 Dolls. B 500. How much does B owe more than A. Ans. 125 Dolls.

4th. From 1000 Take 1.

Rem. 999.

5th.

From 1000 Take 999.

Rem. 1.

6th. A man owed 175 Dolls. ; he paid at one time 50 Dolls; at another, 10; at another, 15; at another, 5; and at another, 3; how much is the balance.

Ans. 92 Dolls.

7th. A bought a Horse of B, for 75 Dolls., a Chaise for 105 Dolls., and Harness for 50 Dolls. He paid as follows, viz. 1 Yoke of Oxen valued at 45 Dolls, one

Cow 15 Dolls., and gave his note for the balance. For how much did he give his note? Ans. 170 Dolls.

8th. A man bought a Cow and Calf for 30 Dolls.; paid 10 Dolls. for keeping her; be sold the Calf for 5 Dolls.. Milk enough to come to 6 Dolls. and used 10 Dolls. worth in his family, then sold the Cow for 18 Dolls. did he gain or lose by the bargain? and how much? Ans. he lost 1 Dol.

SIMPLE MULTIPLICATION.

1. Q What is Simple Multiplication?

A. It is a compendious way of adding; as 3 multiplied by 3 is equal to 9, and is the same as if 3 were set down 3 times and added up.

MULTIPLICATION AND DIVISION TABLE.

DIRECTIONS TO THE PUPIL.

To learn this Table for Multiplication: Look for your Multiplier in the left hand column, and your mul⚫tiplicand at the top, and you will find the product in the square under the multiplicand, on the line against the multiplier: thus; suppose you want to multiply 9 by 6; look for 6 in the left hand column and for 9 at the top, and in the square under 9, against 6, you will find 54, the product.

To learn it for Division: Look for the divisor in the left hand column, and cast your eye along the line to the right hand until you find the dividend; then, directly over the dividend, at the top, you will find the quotient or answer: thus, if you wish to divide 72 by 9, look for 9 in the left hand column and run your eye along the row to the right hand till you find 72, and directly over it, at the top, you will find 8, the quotient.

2. Q. How many numbers must be given to perform Multiplication?

A. Two.

3 Q. Collectively what are they called?
A. Factors.

4. Q. Separately what are they called?

A. The number to be multiplied is called the Multiplicand, and the number by which you multiply is called the Multiplier.

5 Q. What is the number sought called?

A. Product.

6. Q. In what order must the given numbers be plaeed for Multiplication?

A. Place the Multiplier under the Multiplicand with Units under Units, &c. and draw a line below.

7. Q. How do you proceed when the Multiplier is less than 12?

A. Begin at the right hand of the Multiplicand, and multiply each figure contained in it by the Multiplier, setting down all over even tens, and carry as in Addition.

8. Q. How is Multiplication proved?

A. Divide the product by the Multiplier, and if the Quotient be equal to the Multiplicand, the work is right; or it may be proved by casting out the 9's.

9. Q. How is Multiplication proved by casting out

the 9's?

A. Make a cross similar to the sign of Multiplication, cast the nines out of the Multiplicand, and set the remainder at the right hand of the cross; do the same with the Multiplier and set the remainder at the left

! hand of the cross; then multiply the figures at the

right and left of the cross together, cast the 9's out of the product, and set the remainder over the Cross ;also, cast the 9's out of the answer or product of the Multiplicand and Multiplier, and set the remainder under the cross, which will be the same as the figure over it if the work be right.

* In proving this sum by casting out the 9's, I begin at the right hand of the multiplicand and add thus ; 3 & 5 are 8 &8 are 16; 7 above 9; drop the 9, and say 7 & 6 are 13; 4 above 9, drop the 9 again; and after going through the multiplicand in this manner, I find the excess above the 9's to be 7, which I place at the right hand of the cross. The multiplier being less than 9, I place it at the left of the cross. I then say 2X7=14. and set 5, the excess of 9, over the cross. I then cast the 9's out of the product in the same manas I did of the multiplicand, and find the excess to be b, which I place under the cross.

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